A) Analyse the closed loop stability of the system with open loop transfer function {see attachment}
i)Make a sketch of the Bode diagram and hence the full Nyquist diagram, showing all relavent details
ii) If the system is unstable, state the number of closed loop right hand plane poles and comment on how you might stabilise it. If the system is stable, give the gain and phase margins and show these on the Nyquist diagram
iii) Without calculating break-away points, jw crossings etc, make a rough sketch of the root-locus of the above system to confirm your answer in (ii) above.

b) Given an open loop stable L(s), show by making sketches on the Nyquist diagram and the inverse Nichols chart (attached) that for closed loop stability, L(jw) cannot go over the {see attachment} point on the inverse Nichols chart.

*Please see attachments for chart and proper citation of symbols.

Please refer to the attached file. There is a good explanation with necessary Matlab plots. The answer is given assuming the student has basic understanding of the material and the methods, for example: drawing root locus, bode plot and Nyquist diagrams.

(a)

(i)
Transfer function:
-2 s + 2
-----------
0.5 s^2 + s

Bode plot:

There is right hand plane zero at 1 and two poles at 0 and 2. The constant is 2 which equals to 6.02 dB and since there is pole at origin and RHP zero, the bode plot starts at 20+20+6.02= 46.02dB.

Then for the pole at 0 the plot starts falling with a slope of -20dB/dec. For the RHP zero at 1, the plot starts rising with a slope of 20dB/dec. Then again for pole at 2, the plot keeps falling with a slope of -20dB/dec.
The close pole and RHP zero location at 1 and 2 kind of cancels each other affect and the final plot keeps falling with a slope of ...

Solution Summary

This solution is provided in a 5 page, 591 word .doc file attached. It gives the transfer function, bode diagram, nyquist plot, and root locus. Finally, a Nichols chart is provided and explained.

Bodeplot, nyquist,rootlocus. See attached file for full problem description.
A) By drawing the Bode (with reasonable accuracy at frequencies of interest) and then using a rough sketch of the (full) Nyquist diagram, assess the stability of the following system in a unity gain, negative feedback configuration.
b) What wo

Please answer the attached questions regarding linear system stability.
(Involves: loop transfer function; Bodeplot; Nyquist diagram; gain, phase and robust stability margins; positive gain rootlocus).

See attached file for full problem description.
Consider the system with the loop transfer function shown in the attached.
a) Sketch the Bodeplotand calculate (tabulate) L(jw) at w = [0, 1, 5, 10, 40, infinity] rad/s. Hence sketch the full Nyquist diagram.
b) Analyse the closed loop system stability If the closed loop

A feedback loop transfer function is give as:
L(s) = 9 (s+10)/(s+1)(s-30)
Draw the corresponding Bode magnitude and phase angle plots for L(iw) for 0.1plot in the appropriate place of the EdS Chart. Is the closed loop system stable or unstable? Give the precise reasons

Design a proportional and integral controller, G= k_p ((a+1/T_1)/s) for the plant,
P = 1/((X+1)(S+3)) to have dominant poled with (see attachment)
i) Use rough sketches of the rootlocus to determine the location of the controller zero (i.e. find T_1)
ii) Calculate the required controller gain Kp, (An accurate root lo

(Complete problem with equations found in attachment).
Problem 1
A very common industrial controller is the proportional and integral (PI) controller. It has
a transfer function,
, kp is the proportional gain, Ti is the "reset time"
For an integrating process, P(s) = 2/s, investigate the positive rootlocus for

1) G(s) =
Use Matlab and obtain Nyquist Plot
2) G(s) =
Kv1=0.325
Kv2=0.45
Note: K does not equal Kv
Determine the phase margin, gain margin, and closed-loop bandwidth for each case. Determine these both graphically, from the appropriate bodeplots, and using the Matlab functions margin and bandwidth

I am completely lost with Nyquist. I am sure it's a plot of G(s), but when I put the plot in my calculator, it looks nothing like a traditional nyquist plot.
I have a pole at the origin, that is not in the rhp is it? I have a zero in the rhp. So, the number of encirclements is N=#p-#z= so that's -1? There are -1 ccw encir